Answer
$\mathbf{z}=(\frac{7}{2},3,\frac{5}{2})$
Work Step by Step
$\mathbf{u}=(1,2,3)\quad\mathbf{v}=(2,2-1)\quad\mathbf{w}=(4,0,-4)$
Find $\mathbf{z}$ if $2\mathbf{z}-3\mathbf{u}=\mathbf{w}$
We can solve for $\mathbf{z}$:
$2\mathbf{z}=\mathbf{w}+3\mathbf{u}$
$\mathbf{z}=\frac{1}{2}\mathbf{w}+\frac{3}{2}\mathbf{u}$.
All we need to do now is plug in the vectors $\mathbf{w}$ and $\mathbf{u}$:
$\mathbf{z}=\frac{1}{2}(4,0,-4)+\frac{3}{2}(1,2,3)$
$\mathbf{z}=(2,0,-2)+(\frac{3}{2},3,\frac{9}{2})=(\frac{7}{2},3,\frac{5}{2})$
